（毕业设计论文）《抽屉原理及其应用》.doc

抽屉原理及其应用 姓名： 专业：数学与应用数学 学号指导老师： 摘 要：抽屉原理是数学中的重要原理,在解决数学问题时有非常重要的作用.各种形式的抽屉原理在高等数学和初等数学中经常被采用.本文着重从抽屉的构造方法：等分区间、分割图形、利用“对称性” 、 用整数性质、利用染色和根据问题的需要阐述抽屉原理在高等数学和初等数学（竞赛题）中的应用,同时指出了它在应用领域中的不足之处:抽屉的构造有一定的难度,这就要求我们必须要求有一定的数学功底,甚至复杂的需要大量的演算,因此抽屉原理不能充分的运用到我们日常生活中去. 关键词 ：抽屉原理;高等数学; 初等数学 The principle of drawer and its application Abstract：Drawer principle is the important principle of mathematics in solving mathematical problems, has a very important role. All forms of drawer principle in Higher Mathematics and elementary mathematics is often used. This article emphatically from the drawer construction methods: equal interval, segmentation graph, using the symmetry, with properties of the integers, using staining and according to problems on the drawer principle in Higher Mathematics and Elementary Mathematics ( contest ) application, and points out that it is in the field of application of the deficiencies: drawer structure has certain difficulty, this asks we must have some math skills, even complex requires a large amount of calculation, therefore the drawer principle can not full use of our daily life. Key Words：the principle of drawer; advanced mathematics; primary mathematics 目 录 1．抽屉原理 ……………………………………………………….....................1 1.1抽屉原理的简单形式……………………………………………………….............1 1.2抽屉原理的加强形式……………………………………………………….............2 2．抽屉原理的应用 ………………………………………………………...............4 2.1抽屉的构造 ……………………………………………………….....................4 2.2 抽屉原理在数学解题中的应用 ………………………………………………….10 3.抽屉原理在生活中的应用 ………………………………………………………14 3.1月黑穿袜子 ………………………………………………………...................14 3.2手指纹和头发 ………………………………………………………...................14 3.3电脑算命 ………………………………………………………..........................15 4．总结 ………………………………………………………..........................15 参考文献 ………………………………………………………..........................16 致 谢 ………………………………………………………................................17 前言 抽屉原理又叫做鸽巢原理，指的是一件简单明了的事实：为数众多的鸽子飞进为数不多的巢穴里，则至少有一个巢穴飞进了两只或者更多的鸽子。其实有关于抽屉原理（鸽